The present invention pertains to computer numerical controlled (CNC) manufacturing machines and, more particularly, to tool paths along which CNC manufacturing machines move cutting tools to remove material.
Pocket machining is used widely in the aerospace and other industries to mill metal parts. In pocket machining, a pocket is excavated by removing layer(s) of material. As an example, FIG. 1 illustrates a spindle 40 of a CNC manufacturing machine that is carrying a milling tool 42 and is being operated to form a pocket 44 in a layer of material 46. The spindle 40 is rotated about its elongate axis so that the milling tool 42 is rotated, and the spindle is driven along a tool path that is coplanar with the layer of material 46 so that the milling tool engages and cuts into the material (i.e., moves radially into the material). Stated differently, the material 46 is fed into the milling tool 42 due to movement of the spindle 40 along the tool path. Alternatively, the spindle axis may be stationary and the material moved relative to it.
Conventional tool paths can require high axis drive accelerations of the spindle 40 in order to keep feed rates high. This is because conventional tool paths typically include abrupt changes in direction and/or segments that have high local curvature. For example, FIG. 2 schematically illustrates a conventional zig-zag tool path 48a that has been used to remove material, such as to form a rectangular pocket 50a. FIG. 3 schematically illustrates a conventional unidirectional patterned tool path 48b that has been used to remove material, such as to form a rectangular pocket 50b. For the tool path 48b, after each horizontal pass from left to right, the milling tool 42 (FIG. 1) is lifted, moved to the left, and lowered so that it can travel along a different horizontal portion of the tool path 48b. Conventional tool paths 48c, 48d that have been used to remove material, such as to form rectangular pockets 50c, 50d, are schematically illustrated in FIGS. 4 and 5. In contrast to the tool path 48d, for the tool path 48c the milling tool 42 is picked up and moved after traveling along each rectangular portion of the tool path.
Prior tool paths, such as tool paths 48a-d, require high axis drive accelerations in order to have high feed rates, and it is common for the accelerations that are required to exceed the capability of the manufacturing machine and thereby result in lower than optimal feed rates, which is disadvantageous. In addition, prior tool paths that require high accelerations cause greater wear on milling tools 42 than do tool paths requiring lower accelerations, which is disadvantageous.
The present invention solves the above and other problems by providing methods, apparatus and computer readable medium that define and utilize tool paths that have low curvature as compared to conventional tool paths. In accordance with one aspect of the present invention, a spiral tool path is formed by determining a plurality of nested contours that are internal to the boundary of the pocket to be formed, and moving, or most preferably spiraling, between the contours. Whereas several embodiments of the present invention and several aspects of the present invention are described in the context of forming pockets, the invention is not limited to the formation of pockets. For example, the techniques of the present invention can also be used to remove material from raised or other regions, so that pockets are not formed.
In accordance with another aspect of the present invention, the nested contours are determined from a mathematical function. More specifically and in accordance with one example, an offset boundary that the outer boundary extends around is determined, and the mathematical function at least approximates a solution of an elliptic partial differential equation boundary value problem defined on the region enclosed by the offset boundary. In accordance with one embodiment of the present invention, the boundary value problem is a positive definite elliptic partial differential equation eigenvalue problem and the determined mathematical function at least approximates the principal eigenfunction for the positive definite elliptic partial differential equation eigenvalue problem.
In accordance with another aspect of the present invention, the innermost contours are each smooth, with each having low maximum curvature. This measure of curvature generally increases for each subsequent contour closer to the outer boundary.
In accordance with another aspect of the present invention, the spiral tool path includes an orbit that extends around the center of the area bounded by the pocket boundary. The orbit extends from proximate a first one of the contours that extends around the center to proximate a second one of the contours that also extends around the center. The orbit is arranged so that as a ray originating from proximate the center pivots about the center to travel in a first direction along the entire orbit, for a section of the ray extending between the first and second contours, the percentage of the section that extends between the orbit and the first contour continually decreases and the percentage of the section that extends between the orbit and the second contour continually increases.
In accordance with another aspect of the present invention, the orbit is arranged so that while travelling along the entire orbit in a constant direction, the distance from the center either continually increases or continually decreases, but does not alternately increase and decrease.
The present invention advantageously provides low-curvature tool paths, such as spiral tool paths, that allow for the implementation of high feed rates with low acceleration, as compared to conventional designs. In addition, cutting tools that travel along the tool paths defined by the method, apparatus and computer readable medium of the present invention can have relatively low wear rates, as compared to conventional designs.